To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we will combine like terms.
1. The first polynomial:
\[
3 - 2p - 5p^2
\]
2. The second polynomial:
\[
p^4 - 3p + 4
\]
Now, we will rewrite both polynomials and group like terms:
\[
(3 + 4) + (-2p - 3p) + (-5p^2) + (p^4)
\]
This gives us:
- The constant terms: \(3 + 4 = 7\)
- The \(p\) terms: \(-2p - 3p = -5p\)
- The \(p^2\) term: \(-5p^2\)
- The \(p^4\) term: \(p^4\)
Putting it all together, we get:
\[
p^4 - 5p^2 - 5p + 7
\]
So the final expression after adding the two polynomials is:
\[
p^4 - 5p^2 - 5p + 7
\]
The correct response is:
**\(p^4 - 5p^2 - 5p + 7\)**